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Question 19ii) Tut 3

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asked Apr 2 in BUS 4028F - Financial Economics by Kirk (250 points)

How is this index continuously reinvesting dividends different to a normal continuously dividend paying share where we assume dividends are continuously reinvested?  Am I right to say that continuously dividend paying shares continuously reinvest dividends?image

1 Answer

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answered Apr 2 by A.mabaso (600 points)

I have not seen the answer yet but I’d assume that you’re incorrect. 

If a share is continuously reinvesting dividends then what’s essentially happening is that your holding of the share (the number of units you have of the share) would increase continuously.

If you’re not reinvesting the dividends then you would maintain the same number of shares throughout the contract.

commented Apr 2 by Kirk (250 points)
I understand that when you reinvest the dividends in the share continuously that your amount of units in the stock increases continuously.  But we assume this in question 19i) which is what Acted says as per picture below.  So what is the difference in Question 19ii)?  Is it the fact that it is tracking the index or that the future is traded freely or something else?image
commented Apr 2 by A.mabaso (600 points)

So I’ve just had a look at the answer. 

If you want to buy a share in future (forward contract) then the value you are willing to pay is the expected price less any dividends you are not going to receive. That’s what you do for part (i).

This idea comes from the ideas that:

Current Share Price = EPV(Forgone Dividend) + EPV(Future Share Price)

If you want to buy a share and also want the income that was forgone via dividends paid, instead of buying one share you’ll buy one share and a number of units equivalent to the proportion of dividends paid. This is then just the expected value of the share.

Consider a simple case where we have a share currently worth R1000 and we want to enter a forward contract. Let’s say the yearly risk free rate is 5% and that the share will pay a dividend of 10% in 6months time.

The fair price would be the expected price (R1050) less expected dividends paid (R105). So you would be willing to pay R945.

If you’re told that the dividends are reinvested then you would pay for the expected share value R945 and the expected reinvested dividend R105. Which would give you the R1050.

Correct me if anything I did seems fishy. 

commented Apr 2 by Kirk (250 points)

This line of answering does make sense, but I am still confused as to the difference between i) and ii) since according to Acted, the dividend is reinvested in the share if paid continuously which applies to question i).

Thanks for the response and effort.

It is greatly appreciated.

commented Apr 3 by PaulBotes (450 points)

Akani, when you say expected price here in your equation, do you mean with respect to the risk neutral probability measure? Because the expected price of a share does not affect its fair forward price. The forward price is derived independent of a model for the underlying share. 

commented Apr 3 by A.mabaso (600 points)
Yes Paul. I do mean with respect to the risk neutral measure. Thanks.
commented Apr 17 by Faith (580 points)

I am with Kirk here. I still do not understand the difference between what is mentioned in Act Ed and what is required in part ii of question 19.

If i were to apply the formula in acted as referenced on page 21 above, I do not get the same answer as the memo for question 19 ii). 

Please help!